By Dave DeFusco

Designing a great video game is a balancing act, especially in strategy games where the thrill often comes from tackling the unexpected. Whether it’s an enemy ambush or a rare loot drop, the element of surprise keeps players on their toes. But too much randomness can feel unfair, while too little can make a game predictable and boring. Enter the world of probability-driven game design, a method that introduces structured uncertainty into gameplay.

A new framework introduced in the study, “A Flexible Generalized Probability Core and Quantitative Strategy Analysis for Game Design,” by researchers in the Katz School’s Graduate Department of Computer Science and Engineering uses mathematical tools to strike this balance, creating levels that are not only engaging but varied and challenging. The researchers will introduce their new findings at the 2025 IEEE International Conference on Consumer Electronics in January.

In video games, probability controls the outcome of countless actions. Did your attack hit or miss? Will a treasure chest hold gold or junk? By adding a layer of unpredictability, probability makes each playthrough unique. Players are forced to think on their feet, adapt to surprises and develop new strategies. Take games, like XCOM or Star Vikings, where success hinges on a mix of skill and chance. In XCOM, a soldier might have a 90% chance to land a shot—great odds, but still leaving room for failure. These moments inject tension and excitement, making every decision count.

Randomness, when done right, can elevate a game by keeping players engaged. A critical hit, a rare event or an unexpected challenge can make a player’s triumph feel well-earned. Games, like Star Vikings, even let players tweak the odds, such as upgrading characters to improve their chances of success, making randomness a tool they can partially control.

But randomness has a dark side. Missing a high-probability attack at a crucial moment can frustrate players, making them feel cheated. When randomness isn’t communicated clearly—such as unexplained outcomes—it can alienate players who feel they lack control.

“To address these challenges, we propose a probability-based framework that gives game designers precise control over randomness,” said Dr. David Li, senior author of the paper and program director of the M.S. in Data Analytics and Visualization. “The system uses mathematical models, like normal distribution, to generate levels with unique challenges. By adjusting a few parameters, designers can create levels that feel fresh and require different strategies.”

For example, in a strategy game, one level might favor aggressive, high-risk gameplay, while another rewards careful planning. This flexibility helps prevent repetition and keeps players engaged over time. The framework is built on tools from probability theory, including:

• Probability Density Functions (PDF): These help determine how likely an event is to occur. For example, should a player encounter a rare enemy once per level or only once in 10 playthroughs?
• Cumulative Distribution Functions (CDF): These measure the likelihood of events up to a certain point, useful for setting difficulty ramps.

“By using these tools, designers can fine-tune gameplay elements like enemy placement, resource availability or event triggers, ensuring a mix of predictability and surprise,” said Zhengnan Li, a student in the M.S. in Data Analytics and Visualization.

One of the biggest challenges in probability-based games is helping players understand the odds. Games, like XCOM, excel by showing the percentage chance of success for each action. This transparency lets players make informed decisions and accept failures as part of the game. On the flip side, games that hide their probability mechanics, like Darkest Dungeon, risk leaving players feeling frustrated and powerless.

This framework emphasizes clear communication. Whether through visual cues or tutorials, players should know how much chance influences their game—and how they can tilt the odds in their favor.

The framework has already been tested in a prototype, showing its potential to create diverse and engaging levels. For example, the prototype might generate a map where enemies are spaced randomly but with enough clustering to keep players alert. Another might feature resource nodes placed to encourage exploration, but not so predictably that players fall into a routine.

While designed for strategy games, this framework has applications across genres, from role-playing games to shooters. By introducing controlled randomness, it can create dynamic, replayable experiences. The next steps? Applying this model to multiplayer games, where probability could influence everything from team matchups to item spawns. Future research could also explore AI-driven adjustments, personalizing difficulty for individual players.

“Incorporating probability into game design isn’t just about making games harder or more random—it’s about creating a richer, more engaging experience,” said Angela Li of the Applied Mathematics & Physics Department at Stony Brook University. “With tools like this framework, designers can keep players coming back for the thrill of the unexpected, while ensuring the game always feels fair and fun. The magic lies in the perfect mix of skill, strategy and a little bit of luck.”